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6 - We know that a war cannot be waged forcefully on the sea by the soldiers without great danger.

Scimus non sine magno periculo bellum in mari vi geri non posse.

* If I wanted to use the construct Postquam..., does this remain part of the infinitive (postquam oppugnatam esse), or do I need to/can I conjugate the verb and turn the subject into the nominative (postquam oppugnata est)?

Waiting for a week without an answer to perfectly reasonable questions is not a nice experience, so I'll try to answer. But English to Latin is my weakest skill, so make sure you have some grains of salt at the ready!

Tommasinus wrote:1 - We understood that the city, after it had been attacked, was being destroyed by the strength of the soldiers.

Intelleximus urbem oppugnatam* militum vi deleri. * If I wanted to use the construct Postquam..., does this remain part of the infinitive (postquam oppugnatam esse), or do I need to/can I conjugate the verb and turn the subject into the nominative (postquam oppugnata est)?

I think you are right that the participle by itself captures the meaning of "after it had been attacked", but, as you say, you could make it more explicit with postquam. In that case, firstly, subordinate clauses in Indirect Statement generally use finite verbs rather than extending the accusative/infinitive of the main clause; however, the participle would still have to agree with the accusative subject (postquam oppugnatam est). The other question is the mood of the verb. You have probably moved on to unit 7 by now and seen that subordinate clauses in Ind. Statement usually use the subjunctive (unless you are acknowledging the truthfulness of the subordinate clause, which seems reasonable in this example). So it could be oppugnatam est/sit (or oppugnatam erat/esset if you wanted to emphasise the time sequence). M&F make a distinction between vis (power) and the plural vires (strength), so you might use viribus militum, but the dictionaries I have do not make the distinction quite so clear.

2 - Did you hear the rumors that the soldiers were rushing into the cities?

Audivistine rumores milites in oppida ruere?

Looks good to me, although I think urbs is a city, oppidum is a smaller town, so in urbes ruere.

3 - We understand that a model of the city walls has been shown to the men who are about to attack the city with fire and sword.

Now here's an example of potential misinformation from me. I had to look up electos in the dictionary. Found electo, electare to choose/select, and had written that you should correct electos to electatos. It was only by chance that I also found eligo eligere elegi electus to pick out/choose. So beware! (Anyway, M&F probably expected us to use optatos ). The preposition circum is not declined, I think, so it should be circum moenia (urbis) (unless of course you really meant to use the other preposition circa, which also means "around" ). On more solid ground, pugnaturi essent would mean "about to fight' or "be going to fight". I think "that they might fight" would just be the imperfect subjunctive pugnarent.

5 - We shall say that poets should write books not only about Jupiter and Juno, but also about the sea and about the animals of the mountains.

6 - We know that a war cannot be waged forcefully on the sea by the soldiers without great danger.

Scimus non sine magno periculo bellum in mari vi geri non posse.

I think you need cum vī when you don't have an accompanying adjective (you can say magnā vī). And you accidentally left out ā mīlitibus.

A general observation: the books say that the usual order is for a genitive to follow the word on which it depends, unless for reasons of emphasis. So it would be more normal to have, e.g., vi militum in (1), exemplum moenium in (3) etc.